Many tasks require working with coordinate systems. Most often, we are used to the Cartesian coordinate system, where

• the x-axis is directed to the right,

• the y-axis is up.

• the origin of the coordinates is in the center.

However, a different system is used in computer graphics and data processing tasks on the screen:

• x is pointing downwards,

• y is directed to the right,

• the origin is in the upper left corner.

This approach is due to the peculiarities of screens and two-dimensional arrays. Sometimes tasks require converting this system to a Cartesian one, where the center of the screen becomes the origin. Suppose we have a screen with a height of n and a width of m pixels. The center of the screen is at the point (n / 2, m / 2).

To switch from screen coordinates (x0,y0) to Cartesian coordinates (x,y), the following formula is used:

x = y0 — m / 2

y = — (x0 — n / 2)

It is important to keep in mind that the division in this case is an integer.